Chaotic Dynamics of the Mass Deformed ABJM Model

Abstract

We explore the chaotic dynamics of the mass deformed ABJM model. To do so, we first perform a dimensional reduction of this model from 2 + 1-to 0 + 1dimensions, considering that the fields are spatially uniform. Working in the 't Hooft limit and tracing over ansatz configurations involving fuzzy two spheres, which are described in terms of the GRVV matrices with collective time dependence, we obtain a family of reduced effective Lagrangians and demonstrate that they have chaotic dynamics by computing the associated Lyapunov spectrum. In particular, we analyze in detail, how the largest Lyapunov exponent, λ L , changes as a function of E/N 2 . Depending on the structure of the effective potentials, we find either, where γ N (k, µ) is a constant determined in terms of the Chern-Simons coupling k, the mass µ, and the matrix level N . Using our results, we investigate the temperature dependence of the largest Lyapunov exponents and give upper bounds on the temperature above which λ L values comply with the MSS bound, λ L ≤ 2πT , and below which it will eventually be violated.

Chaos in Matrix Gauge Theories with Massive Deformations

“…Let us also note that, recently, we have also studied the chaotic dynamics emerging from the mass deformed ABJM model using similar methods and found that the Lyapunov exponents vary either 𝜆 𝐿 ∝ (𝐸/𝑁 2 ) 1/3 or 𝜆 𝐿 ∝ (𝐸/𝑁 2 − 𝛾 𝑁 ) 1/3 , where 𝛾 𝑁 (𝑘, 𝜇) is a constant determined in terms of the parameters of this model. Our results, including the critical temperature in regard to the MSS bound are presented in the article [42].…”

Classical and quantum butterfly effect in nonlinear vector mechanics

“…Finally, note that the model (1.3) is very similar to some spatially reduced string and gauge models [93,[99][100][101][102][103][104][105][106][107][108][109]. In particular, the N = 3 variant of (1.3) is nothing but a spatially reduced SU (2) Yang-Mills [99], which is known to possess a nonzero classical Lyapunov exponent κ ∼ 4 √ E, see [93,[100][101][102].…”

Chaos in the Mass-Deformed ABJM Model

“…4π is no longer level quantized. A more comprehensive discussion on the latter fact may be found in [9].…”

“…In a more recent paper [9], we have examined chaos emerging from the massive deformation of the Aharony-Bergman-Jafferis-Maldacena (ABJM) model. Here, I will be reporting on a part of this work.…”